Germany · Klasse 10 · Practice Sheet 44

1. 1.

   A cone has base radius 12 cm and height 19 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

   $V = \tfrac{1}{3} \pi r^2 h$

   View formula →
2. 2.

   Find the gravitational potential energy of a 46 kg object raised 18 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

   View formula →
3. 3.

   A wave has frequency 858 Hz and wavelength 3.54 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

   View formula →
4. 4.

   Find the sum of the first 18 terms of an arithmetic series with first term a = 2 and common difference d = 8.

   Formula:Sum of an Arithmetic Series

   $S_n = \tfrac{n}{2}\left(2a + (n-1)d\right)$

   View formula →
5. 5.

   Find the volume of a sphere of radius 5 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

   $V = \tfrac{4}{3} \pi r^3$

   View formula →
6. 6.

   A triangle has sides a = 13 cm and b = 18 cm with an included angle C = 120°. Find its area (to 2 d.p.).

   Formula:Area of a Triangle (Sine Rule)

   $A = \tfrac{1}{2} ab\sin C$

   View formula →
7. 7.

   A force of 277 N acts on an area of 7.4 m². Find the pressure.

   Formula:Pressure

   $P = \dfrac{F}{A}$

   View formula →
8. 8.

   €1,700 is invested at 4% compound interest per annum for 2 years. Find the final amount (to 2 d.p.).

   Formula:Compound Interest

   $A = P\left(1 + \dfrac{r}{100}\right)^{t}$

   View formula →
9. 9.

   A bag has 24 equally likely marbles, of which 18 are red. Find the probability of drawing a red marble (to 3 d.p.).

   Formula:Simple Probability

   $P(E) = \dfrac{\text{favourable}}{\text{total}}$

   View formula →
10. 10.

    Find the momentum of a 36 kg object moving at 2 m/s.

    Formula:Momentum

    $p = mv$

    View formula →
11. 11.

    A force of 419 N acts on an area of 8.1 m². Find the pressure.

    Formula:Pressure

    $P = \dfrac{F}{A}$

    View formula →
12. 12.

    A bag has 19 equally likely marbles, of which 9 are red. Find the probability of drawing a red marble (to 3 d.p.).

    Formula:Simple Probability

    $P(E) = \dfrac{\text{favourable}}{\text{total}}$

    View formula →
13. 13.

    A triangle has sides a = 8 cm and b = 5 cm with an included angle C = 120°. Find its area (to 2 d.p.).

    Formula:Area of a Triangle (Sine Rule)

    $A = \tfrac{1}{2} ab\sin C$

    View formula →
14. 14.

    A bag has 9 equally likely marbles, of which 1 are red. Find the probability of drawing a red marble (to 3 d.p.).

    Formula:Simple Probability

    $P(E) = \dfrac{\text{favourable}}{\text{total}}$

    View formula →
15. 15.

    A body starts at 3 m/s and accelerates at 5.9 m/s² for 12 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

    View formula →
16. 16.

    Solve for x: 4x + 15 = 23.

    Formula:Solving a Linear Equation

    $x = \dfrac{c - b}{a}$

    View formula →
17. 17.

    A 27 kg object moves at 23 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

    $KE = \tfrac{1}{2} m v^2$

    View formula →
18. 18.

    Find the momentum of a 60 kg object moving at 22 m/s.

    Formula:Momentum

    $p = mv$

    View formula →
19. 19.

    A right-angled triangle has legs of 18 cm and 15 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

    $c = \sqrt{a^2 + b^2}$

    View formula →
20. 20.

    A population of 7,500 grows 3% per year. Find its size after 4 years (nearest whole number).

    Formula:Exponential Growth

    $N = N_0 (1 + r)^{t}$

    View formula →

© FormulaWon — formulawon.app · Answers & step-by-step working available on the solutions sheet.